Decentralized Modeling

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Decentralized Modeling and Decentralized Thinking

Mitchel ResnickMIT Media [email protected]

Published in:Modeling and Simulation in Precollege Science and Mathematics (pp. 114-137),

edited by W. Feurzeig and N. Roberts. Springer: New York.

1. Introduction: The Era of Decentralization

It seems fair to say that we live in an Era of Decentralization. Almost every time youpick up a newspaper, you can see evidence of the growing interest in decentralizedsystems. On the front page, you might read an article about the transition of the formerCommunist states from centrally-planned economies to market-based economies. Turn to

the business page, and you might find an article about the shift in corporate organizationsaway from top-down hierarchies toward decentralized management structures. Thescience section might carry an article about new distributed models of the mind, and itmight include a technology column about the role of the Internet in promoting distributedapproaches to computing. And in the book review, you might discover how the latestliterary theories are based on the idea that literary meaning itself is decentralized, alwaysconstructed by individual readers, not imposed by a centralized author.

But even as the influence of decentralized ideas grows within our culture, there is adeep-seated resistance to such ideas. At some deep level, people seem to have strongattachments to centralized ways of thinking. When people see patterns in the world, they

often assume that there is some type of centralized control, even when it doesnt exist.For example, most people assume that birds in a flock play a game of follow-the-leader:the bird at the front of the flock leads, and the others follow. But thats not so. In fact,most bird flocks dont have leaders at all. Rather, each bird follows a set of simple rules,reacting to the movements of the birds nearby it. Orderly flock patterns arise from thesesimple, local interactions. The bird in front is not a leader in any meaningful senseitjust happens to end up there. The flock is organized without an organizer, coordinatedwithout a coordinator. Yet most people continue to assume the existence of a leaderbird.

This assumption of centralized control, a phenomenon I call the centralized mindset, isnot just a misconception of the scientifically naive. It seems to affect the thinking ofnearly everyone. Until recently, even scientists assumed that bird flocks must haveleaders. It is only in recent years that scientists have revised their theories, asserting thatbird flocks are leader-less and self-organized (Heppner and Grenander, 1990; Reynolds,1987). A similar bias toward centralized theories can be seen throughout the history ofscience.

In this chapter, I discuss how computer-modeling activities can help people movebeyond the centralized mindset, helping them gain new insights into (and appreciation


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Principle 4: Facilitate personal connections (not just mathematical abstractions). Indesigning new types of learning tools, it is important to consider two types ofconnections (Resnick, Bruckman, and Martin, 1996). First, there are epistemologicalconnections: how will the tool connect to important domains of knowledge andencourage new ways of thinking? But equally important are personal connections: how

will the tool connect to users interests, passions, and experiences? Many computer-modeling tools are impersonal: students must manipulate either mathematicalabstractions or aggregate quantities. StarLogo aims to be more personal, encouragingstudents to think about the actions and interactions of individual (and familiar) objects.

Principle 5: Focus on stimulation (not just simulation). Many computer models try toimitate some real-word system or process as accurately as possible. Computersimulations of nuclear reactors are used to predict when the reactors might fail; computersimulations of meteorological patterns are used to predict tomorrows weather. In thesecases, the more accurate the simulation, the better. But, for educational applications ofcomputer modeling, real-world fidelity should not be the top goal. Instead, the real worldshould serve only as an inspiration, a departure point for thinking about some set of ideas

or concepts. The goal is not to simulate particular systems and processes in the world; itis to probe, challenge, and disrupt the way people think about systems and processes ingeneral. That is the goal of StarLogo: to stimulate people to develop new ways ofthinking about decentralized systems.

3. The Centralized Mindset

Before exploring how computer modeling can help people move beyond thecentralized mindset, it is worth examining the nature of the centralized mindset. In someways, the pervasiveness of the centralized mindset might seem surprising. After all,arent we living in an Era of Decentralization? Actually, it isnt so surprising if we look

at the growing interest in decentralization from a different perspective: Why are peoplebecoming more interested in decentralized ideas now? Why didnt it happen before? Whyhave people resisted decentralized approaches in the past? What underlies thispersistence of resistance? What made people cling onto centralized approaches so tightly,for so long?

The centralized mindset can be seen throughout the history of science. Until the mid-19th century, almost everyone embraced the idea that living systems were designed bysome God-like entity. Even scientists were convinced by the so-called watchmakerargument (or the argument from design), proposed by theologian William Paley in hisbook Natural Theology (Paley, 1802). Paley noted that watches are very complex and

precise objects. If you found a watch on the ground, you could not possibly believe thatsuch a complex object had been created by random chance. Instead, you would naturallyconclude that the watch must have ad a maker. For Paley, the same logic applies to livingsystems: they, too, must have a maker.

It is not surprising that scientists accepted Paleys argument in the early 19th century,since there were no viable alternative explanations for the complexity of living systems.What is surprising is how strongly scientists held onto centralized beliefs even after


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Darwin provided a viable (and more decentralized) alternative. Science historian ErnstMayr (1982) notes that biologists put up enormous resistance to Darwins theories for afull 80 years after publication of Origin of Species, generally preferring more centralizedalternatives.

The history of research on slime-mold cells, as told by Evelyn Fox Keller (1985),provides another example of centralized thinking. During their life cycle, slime-moldcells sometimes gather together into clusters. For many years, scientists believed that theaggregation process was coordinated by specialized slime-mold cells, known asfounder or pacemaker cells. According to this theory, each pacemaker cell sends outa chemical signal, telling other slime-mold cells to gather around it, resulting in a cluster.In 1970, Keller and Segel (1970) proposed an alternative model, showing how slime-mold cells can aggregate without any specialized cells. Nevertheless, for the followingdecade, other researchers continued to assume that special pacemaker cells were requiredto initiate the aggregation process. As Keller (1985) writes, with an air of disbelief: Thepacemaker view was embraced with a degree of enthusiasm that suggests that thisquestion was in some sense foreclosed. By the early 1980s, researchers began to accept

the idea of aggregation among homogeneous cells, without any pacemaker. But thedecade-long resistance serves as some indication of the strength of the centralizedmindset.

People also view the workings of the economy in centralized ways, assuming singularcauses for complex phenomena. Children, in particular, seem to assume stronggovernmental control over the economy. Of course, governments doplay a large role inmost economies, but children assume that governments play an even larger role than theyactually do. In interviews with Israeli children between 8 and 15 years old, psychologistDavid Leiser (1983) found that nearly half of the children assumed that the governmentsets all prices and pays all salaries. Even children who said that employers pay salaries

often believed that the government provides the money for the salaries. A significantmajority of the students assumed that the government pays the increased salaries after astrike. And many younger children had the seemingly contradictory belief that thegovernment is also responsible for organizing strikes. As Leiser writes: The child findsit easier to refer unexplained phenomena to the deliberate actions of a clearly definedentity, such as the government, than to impersonal market forces.

In some ways, it is not surprising that people have such strong commitments tocentralized approaches. Many phenomena in the world are, in fact, organized by a centraldesigner. These phenomena act to reinforce the centralized mindset. When people seeneat rows of corn in a field, they assume (correctly) that the corn was planted by afarmer. When people watch a ballet, they assume (correctly) that the movements of the

dancers were planned by a choreographer. When people see a watch, they assume(correctly) that it was designed by a watchmaker.

Moreover, most people participate in social systems (such as families and schoolclassrooms) where power and authority are very centralized. These hierarchical systemsserve as strong models. Many people are probably unaware that other types oforganization are even possible. In an earlier research project, I developed a programminglanguage (called MultiLogo) based on agents that communicated with one another. In


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To engage students in thinking about decentralized systems, I wanted to provide anenvironment similar to cellular automata, but more connected to students interests andexperiences. While cellular automata are well-suited for computer hackers andmathematicians, they seem ill-suited for people who have less experience (or less interestin) manipulating abstract systems. The objects and operations in cellular automata are not

familiar to most people. The idea of writing transition rules for cells is not an ideathat most people can relate to.

Instead, I decided to create an environment based on the familiar ideas of creaturesand colonies. The goal was to enable students to investigate the ways that colony-levelbehaviors (such as bird flocks or ant foraging trails) can arise from interactions amongindividual creatures.1 Logo seemed like a good starting point for my computationalsystem (Papert, 1980; Harvey, 1985). The traditional Logo turtle can be used torepresent almost any type of object in the world: an ant in a colony, a car in a traffic jam,an antibody in the immune system, or a molecule in a gas. But traditional versions of theLogo language are missing several key features that are needed for explorations ofcolony-type behaviors. So I developed a new version of Logo, called StarLogo, that

extends Logo in three major ways (Resnick, 1991, 1994).

First, StarLogo has many more turtles. While commercial versions of Logo typicallyhave only a few turtles, StarLogo has thousands of turtles, and all of the turtles canperform their actions at the same time, in parallel.2For many colony-type explorations,having a large number of turtles is not just a nicety, it is a necessity. In many cases, thebehavior of a colony changes qualitatively when the number of creatures is increased. Anant colony with 10 ants might not be able to make a stable pheromone trail to a foodsource, whereas a colony with 100 ants (following the exact same rules) might.

Second, StarLogo turtles have better senses. The traditional Logo turtle was

designed primarily as a drawing turtle, for creating geometric shapes and exploringgeometric ideas. But the StarLogo turtle is more of a behavioral turtle. StarLogo turtlescome equipped with senses. They can detect (and distinguish) other turtles nearby, andthey can sniff scents in the world. Such turtle-turtle and turtle-world interactions areessential for creating and experimenting with decentralized and self-organizingphenomena. Parallelism alone is not enough. If each turtle just acts on its own, withoutany interactions, interesting colony-level behaviors will generally not arise.

Third, StarLogo reifies the turtles world. In traditional versions of Logo, the turtlesworld does not have many distinguishing features. The world is simply a place where theturtles draw with their pens. Each pixel of the world has a single piece of stateinformationits color. StarLogo attaches a much higher status to the turtles world. The

1 I am using the terms creature and colony rather broadly. On a highway, each car can beconsidered a creature, and a traffic jam can be considered the colony.

2The initial version of StarLogo was implemented on a massively-parallel computer, the ConnectionMachine. We have since implemented StarLogo on traditional sequential computers by simulating

parallelism. To download a copy of StarLogo, see http://www.media.mit.edu/~starlogo/


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world is divided into small square sections calledpatches. The patches have many of thesame capabilities as turtles, except that they can not move. Each patch can hold anarbitrary variety of information. For example, if the turtles are programmed to release achemical as they move, each patch can keep track of the amount of chemical that hasbeen released within its borders. Patches can execute StarLogo commands, just as turtles

do. For example, each patch could diffuse some of its chemical into neighboringpatches, or it could grow food based on the level of chemical within its borders. Thus,the environment is given a status equal to that of the creatures inhabiting it.

StarLogo programs can be conceptualized as turtles moving on top of (and interactingwith) a cellular-automata grid. All types of interactions are possible: turtle-turtle, turtle-patch, and patch-patch interactions. StarLogo places special emphasis on localinteractionsthat is, interactions among turtles and patches that are spatially near oneanother. Thus, StarLogo is well-suited for explorations of self-organizing phenomena, inwhich large-scale patterns arise from local interactions. In addition, the massivelyparallel nature of StarLogo makes it well-suited for explorations of probabilistic andstatistical conceptsand studies of peoples thinking about these concepts (Wilensky,

1993).

Figure 1 shows a StarLogo simulation of slime-mold cells aggregating into clusters. Inthis example, each cell emits a chemical pheromone, and it also moves in the directionwhere the pheromone is strongest (that is, it follows the gradient of the pheromone). Atthe same time, the patches cause the pheromone to diffuse and evaporate. With thissimple strategy, the cells quickly aggregate into clustersdemonstrating that aggregationcan arise from a decentralized mechanism.

In some ways, the ideas underlying StarLogo parallel the ideas underlying the earlyversions of Logo itself. In the late 1960s, Logo aimed to make then-new ideas from the

computer-science community (like procedural abstraction and recursion) accessible to alarger number of users. Similarly, StarLogo aims to make 1990s ideas from computerscience (like massive parallelism) accessible to a larger audience. And whereas Logointroduced a new object (the turtle) to facilitate explorations of particularmathematical/scientific ideas, such as differential geometry (Abelson & diSessa, 1980),StarLogo introduces another new object (the patch) to facilitate explorations of othermathematical/scientific ideas (such as self-organization).


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t = 0 t = 20 t = 40

t = 60 t = 80 t = 100

Figure 1: Slime-mold cells aggregating into clusters

5. StarLogo Stories

This section presents stories of student projects with StarLogodescribing the modelsthat students constructed and what they learned in doing so. The students typically cameto MIT for eight to ten sessions, each lasting 60 to 90 minutes. Most students workedtogether in pairs. I worked directly with the students, suggesting projects, askingquestions, challenging assumptions, helping with programming, and encouragingstudents to reflect on their experiences as they worked with StarLogo. Computerinteractions were saved in computer files, and all discussions were recorded on audiotape. In the early sessions, I typically showed students existing StarLogo programs. Thestudents experimented with the programs, trying different parameters and making slightmodifications of the programs. As the sessions progressed, I encouraged students todevelop their own projects ideas and construct their own models, based on personalinterests.

5.1 Traffic Jams

Ari and Fadhil were students at a public high-school in the Boston area. Both enjoyedworking with computers, but neither had a very strong mathematical or scientific


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background. At the time Ari and Fadhil started working with StarLogo, they were alsotaking a drivers education class. Each had turned 16 years old a short time before, andthey were excited about getting their drivers licenses. Much of their conversationfocused on cars. When I gave Ari and Fadhil a collection of articles to read, a ScientificAmerican article titled Vehicular Traffic Flow (Herman & Gardels, 1963) captured

their attention.

Traffic flow is rich domain for studying collective behavior. Interactions among carsin a traffic flow can lead to surprising group phenomena. Consider a long road with nocross streets or intersections. What if we added some traffic lights along the road? Thetraffic lights would seem to serve no constructive purpose. It would be natural to assumethat the traffic lights would reduce the overall traffic throughput (number of cars per unittime). But in some situations, additional traffic lights actually improve overall trafficthroughput. The New York City Port Authority, for example, found that it could increasetraffic throughput in the Holland Tunnel by 6 percent by deliberately stopping some carsbefore they entered the tunnel (Herman & Gardels, 1963).

Traditional studies of traffic flow rely on sophisticated analytic techniques (from fieldslike queuing theory). But many of the same traffic phenomena can be explored withsimple StarLogo programs. To get started, Ari and Fadhil decided to create a one-lanehighway. (Later, they experimented with multiple lanes.) Ari suggested adding a policeradar trap somewhere along the road, to catch cars going above the speed limit. But healso wanted each car to have its own radar detector, so that cars would know to slowdown when they approached the radar trap.

After some discussion, Ari and Fadhil decided that each StarLogo turtle/car shouldfollow three basic rules:

If there is a car close ahead of you, slow down.

If there are not any cars close ahead of you, speed up (unless you arealready moving at the speed limit).

If you detect a radar trap, slow down.

Ari and Fadhil implemented these rules in StarLogo. They expected that a traffic jamwould form behind the radar trap, and indeed it did (Figure 2). After a few dozeniterations of the StarLogo program, a line of cars started to form to the left of the radartrap. The cars moved slowly through the trap, then sped away as soon as they passed it.Ari explained: First one car slows down for the radar trap, then the one behind it slows

down, then the one behind that one, and then youve got a traffic jam.

I asked Ari and Fadhil what would happen if onlysomeof the cars had radar detectors.Ari predicted that only some of the cars would slow down for the radar trap. Fadhil had adifferent idea: The ones that have radar detectors will slow down, which will cause theother ones to slow down. Fadhil was right. The students modified the StarLogo programso that only 25 percent of the cars had radar detectors. The result: the traffic flow lookedexactly the same as when all of the cars had radar detectors.


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t = 0

t = 10

t = 20

t = 30

t = 40

t = 50

t = 60

t = 70

Figure 2: Traffic jam caused by radar trap (shaded area)(Cars move left to right)

What if noneof the cars had radar detectorsor, equivalently, if the radar trap wereremoved entirely? With no radar trap, the cars would be controlled by just two simplerules: if you see another car close ahead, slow down; if not, speed up. The rules could notbe much simpler. At first, Fadhil predicted that the traffic flow would become uniform:cars would be evenly spaced, traveling at a constant speed. Without the radar trap, hereasoned, what could cause a jam? But when the students ran the program, a traffic jamformed (Figure 3). Along parts of the road, the cars were tightly packed and movingslowly. Elsewhere, they were spread out and moving at the speed limit.

Ari and Fadhil were surprised. And when I showed Ari and Fadhils program to otherhigh-school students, they too were surprised. In general, the students expected the carsto end up evenly spaced along the highway, separated by equal distances. Several of them

talked about the cars reaching an equilibrium, characterized by equal spacing. No oneexpected a traffic jam to form. Some of their predictions:

Emily: [The cars will] just speed along, just keep going along...they willend up staggered, in intervals.

Frank: Nothing will be wrong with it. Cars will just go...Theres noobstacles. The cars will just keep going, and thats it.


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Ramesh: They will probably adjust themselves to a uniform distance fromeach other.

When I ran the simulation, and traffic jams began to form, the students were shocked.

In their comments, most students revealed a strong commitment to the idea that sometype of seed (like an accident or a broken bridge) is needed to start a traffic jam.Perhaps Frank expressed it best: I didnt think there would be any problem, since therewas nothing there. If there is nothing thereif there is no seedthere should not be atraffic jam. Traffic jams do not just happen; they must have localizable causes. And thecause must come from outside the system (not from the cars themselves). Someresearchers who study systems talk about exogenous(external) and endogenous(internal)factors affecting the behavior of a system. In the minds of the students, patterns (such astraffic jams) can be formed only by exogenous factors.

Fadhil suggested that the jams were caused by differences in the initial speeds of the

cars. So the students changed the StarLogo program, starting all of the cars at the exactsame speed. But the jams still formed. Fadhil quickly understood. At the beginning of theprogram, the cars were placed at random positions on the road. Random positioning ledto uneven spacing between the cars, and uneven spacing could also provide the seedfrom which a traffic jam could form. Fadhil explained: Some of the cars start closer toother cars. Like, four spaces between two of them, and two spaces between others. A carthats only two spaces behind another car slows down, then the one behind it slowsdown.

t = 0

t = 10

t = 20

t = 30

t = 40

t = 50

t = 60

t = 70

Figure 3: Traffic jam without radar trap(Cars move left to right, but jam moves right to left)


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average of 44 wood chips in each pile. The process was rather slow, and it was frustratingto watch, as termites often carried wood chips away from well-established piles. But, allin all, the program worked quite well.

Why did it work? As we watched the program, it suddenly seemed obvious. Imaginewhat happens when the termites (by chance) remove all of the wood chips from aparticular pile. Because all of the wood chips are gone from that spot, termites will neveragain drop wood chips there. So the pile has no way of restarting.

As long as a pile exists, its size is a two-way street: it can either grow or shrink. Butthe existenceof a pile is a one-way street: once it is gone, it is gone forever. Thus, a pileis somewhat analogous to a species of creatures in the real world. As long as the speciesexists, the number of individuals in the species can go up or down. But once all of theindividuals are gone, the species is extinct, gone forever. In these cases, zero is atrapped state: once the number of creatures in a species (or the number of wood chipsin a pile) goes to zero, it can never rebound.

Of course, the analogy between species and piles breaks down in some ways. Newspecies are sometimes created, as offshoots of existing species. But in the termiteprogram, there is no way to create a new pile. The program starts with roughly 2000wood chips. These wood chips can be viewed as 2000 piles, each with a single woodchip. As the program runs, some piles disappear, and no new piles are created. So thetotal number of piles decreases monotonically.

ITERATIONS

5000 10000 15000

400

300

200

100

NUMBER

OF

PILES

Figure 4: The number of piles decreases monotonically


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5.3 Rabbits and Grass

The great baseball manager Casey Stengel once said: If you dont know where youregoing, you might end up somewhere else. My experiences with computer-basedmodeling activities have taught me a corollary: Even if you think you know whereyoure going, youll probably end up somewhere else.

Thats what happened to Benjamin, a high-school student, when he set out to create anStarLogo program that would simulate evolution by natural selection. I had givenBenjamin a Scientific American article (Dewdney, 1989) about a computer programcalled Simulated Evolution(Palmiter, 1989). Benjamin, who had just finished his junioryear in high school, decided that he wanted to create a StarLogo program similar to thecommercial program described in the article. His goal was to create a set of computercreatures that would interact and evolve.

At the core of Benjamins simulation were turtles and food. His basic idea was simple:turtles that eat a lot of food reproduce, and turtles that dont eat enough food die.

Eventually, he planned to add genes to his turtles. Different genes could provide turtleswith different levels of fitness (perhaps different capabilities for finding food). ButBenjamin never got around to the genes. Rather, on the road to evolution, Benjamin gotsidetracked into an interesting exploration of ecological systems (in particular, predator-prey systems).

Benjamin began by making food grow randomly throughout the StarLogo world.(During each time step, each StarLogo patch had a random chance of growing somefood.) Then he created some turtles. The turtles had very meager sensory capabilities.They could not see or smell food at a distance. They could sense food only whenthey bumped directly into it. So the turtles followed a very simple strategy: Wanderaround randomly, eating whatever food you bump into.

Benjamin gave each turtle an energy variable. Every time a turtle took a step, itsenergy decreased a bit. Every time it ate some food, its energy increased. Then Benjaminadded one more rule: if a turtles energy dipped to zero, the turtle died. With thisprogram, the turtles do not reproduce. Life is a one-way street: turtles die, but no newturtles are born. Still, even with this simple-minded program, Benjamin found somesurprising and interesting behaviors.

Benjamin ran the program with 300 turtles. But the environment could not support thatmany turtles. There wasnt enough food. So some turtles began to die. The turtlepopulation fell rapidly at first, then it leveled out at about 150 turtles. The system seemed

to reach a steady state with 150 turtles: the number of turtles and the density of food bothremained roughly constant.

Then Benjamin tried the same program with 1000 turtles. If there wasnt enough foodfor 300 turtles, there certainly wouldnt be enough for 1000 turtles. So Benjamin wasntsurprised when the turtle population began to fall. But he wassurprised with howfarthepopulation fell. After a while, only 28 turtles remained. Benjamin was puzzled: Westarted with more, why should we end up with less? After some discussion, he realized


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what had happened. With so many turtles, the food shortage was even more critical thanbefore. The result: mass starvation. Benjamin still found the behavior a bit strange: Theturtles have less (initial energy as a group), and less usually isnt more.

Next, Benjamin decided to add reproduction to his model. His plan: whenever aturtles energy increases above a certain threshold, the turtle should clone itself, andsplit its energy with its new twin. That can be accomplished by adding another demonprocedure to the program.

Benjamin assumed that the rule for cloning would somehow balance the rule fordying, leading to some sort of equilibrium. He explained: Hopefully, it will balanceitself out somehow. I mean it will. It will have to. But I dont know what number it willbalance out at. After a little more thought, Benjamin suggested that the food supplymight fall at first, but then it would rise back and become steady: The food will godown, a lot of them will die, the food will go up, and it will balance out.

Benjamin started the program running. As Benjamin expected, the food supply

initially went down and then went up. But it didnt balance out as Benjamin hadpredicted: it went down and up again, and again, and again. Meanwhile, the turtlepopulation also oscillated, but out of phase with the food.

On each cycle, the turtles overgrazed the food supply, leading to a scarcity of food,and many of the turtles died. But then, with fewer turtles left to eat the food, the foodbecame more dense. The few surviving turtles thus found a plentiful food supply, andeach of them rapidly increased its energy. When a turtles energy surpassed a certainthreshold, it cloned, increasing the turtle population. But as the population grew too high,food again became scarce, and the cycle started again.

Visually, the oscillations were striking. Red objects (turtles) and green objects (food)were always intermixed, but the density of each continually changed. Initially, the screenwas dominated by red turtles, with a sparse scattering of green food. As the density of redobjects declined, the green objects proliferated, and the screen was soon overwhelminglygreen. Then the process reversed: the density of red increased, with the density of greendeclined.

Depending on the particular parameters, the oscillations took on different forms. InBenjamins initial program, the oscillations were damped: With each cycle, the peakswere a little less high, the troughs a little less deep. In the first cycle, the turtle populationdwindled to just 26 turtles, then it rose to 303 turtles. In the next cycle, the populationshrank to 47 turtles, then up to 244 turtles. Eventually, the turtle population stabilized

between 130 and 160 turtles.

Benjamin recognized that this result depended critically on the parameters in hisStarLogo program. He wondered: What would happen if the food grew just half asquickly? He figured that this new world would support fewer turtles, but how manyfewer? In the original version of his StarLogo program, each patch had a 1 in 1000chance of growing food. Benjamin changed it to 1 in 2000.


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When Benjamin ran the program, he was in for another surprise: all of the turtles died.But Benjamin, who had just finished graphing the oscillations from the previousexperiment, quickly realized what had happened. The oscillation must be between somenumber and negative something, he said. That is: the trough of the oscillation must dropbelow zero. And once the population drops below zero, it can never recover. There is no

peak after a negative trough. Extinction is forever: it is a trapped state.

The problem lay in the initial conditions. Benjamin had started the simulation with1000 turtles. If there were fewer initial turtles, the first trough wouldnt sink so deep.Benjamin came up with an ingenious solution. Ill start with just one (turtle), heexplained. It will definitely survive. Ill put money on it. Benjamin started the programagain, this time with a single turtle. For a while, the single turtle roamed the world byitself. Benjamin cheered it on: Come on. Hang on there. Come on. Get some food.Finally, the turtle cloned, and then there were two. Hes going to live, exclaimedBenjamin.

The turtle population rose to about 130 turtles, leveled off, then fell. As before, the

turtle population went up and down in a damped oscillation. Eventually, the populationstabilized at about 75 turtles. So with food growing at half the rate as before, the turtlepopulation stabilized at about half the level as before. The equilibrium populationseemed to be proportional to the rate of food growth.

Before running the program, Benjamin had predicted that the equilibrium populationwould be more drastically affected by the reduction in food growth. He expected thepopulation to stabilize with considerably fewer than 75 turtles. But after watching theprogram run, he developed a explanation for the proportional relationship. Looking at thedots of food on the screen, he noted that the food density at equilibrium looked aboutthe same as in the previous experiment, despite the change in the rate of food growth.

That made sense to him: a certain food density is needed to keep the turtles just on thebrink between death and reproduction. To reach a relatively steady state, the systemneeded to maintain that special food density. Given that the food was growing just half asquickly as before, it made sense that the system could support only half as many turtles.

Benjamins reasoning is an example of what Hut and Sussman (1987) dubbedanalysis by synthesis. Traditionally, synthesis and analysis have been seen inopposition to one another, two alternate ways of solving problems. But with computer-based explorations, the two approaches get mixed and blurred. It is very unlikely thatBenjamin could have developed his explanation without actually viewing (andmanipulating) the simulation. Only by building and creating (synthesis) was Benjaminable to develop a well-reasoned explanation for the behavior of the turtles (analysis).

The oscillating behavior in Benjamins project is characteristic of ecological systemswith predators (in this case, turtles) and prey (in this case, food). Traditionally, scientific(and educational) explorations of predator-prey systems are based on sets of differentialequations, known as the Lotka-Volterra equations (Lotka 1925; Volterra 1926). Forexample, the changes in the population density of the prey (n1) and the population

density of the predator (n2) can be described with the following differential equations:


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dn1/dt = n1(b - k1n2)

dn2/dt = n2(k2n1- d)

where bis the birth rate of the prey, dis the death rate of the predators, and k1and k2

are constants. It is straightforward to write a computer program based on the Lotka-Volterra equations, computing how the population densities of the predator and prey varywith time (e.g., Roberts 1983).

This differential-equation approach is typical of the way that scientists havetraditionally modeled and studied the behaviors of all types of systems (physical,biological, and social). Scientists typically write down sets of differential equations thenattempt to solve them either analytically or numerically. These approaches requireadvanced mathematical training; usually, they are studied only at the university level.

The StarLogo approach to modeling systems (exemplified by Benjamins project) issharply different. StarLogo makes systems-related ideas more accessible to younger

students by providing them with a stronger personal connection to the underlying models.Traditional differential-equation approaches are impersonal in two ways. The first isobvious: they rely on abstract symbol manipulation (accessible only to students withadvanced mathematical training). The second is more subtle: differential equations dealin aggregate quantities. In the Lotka-Volterra system, for example, the differentialequations describe how the overallpopulations(not the individual creatures) evolve overtime. There are now some very good computer modeling toolssuch as Stella (Robertset al., 1983) and Model-It (Jackson et al., 1996)based on differential equations. Thesetools eliminate the need to manipulate symbols, focusing on more qualitative andgraphical descriptions. But they still rely on aggregate quantities.

In StarLogo, by contrast, students think about the actions and interactions of individualobjects or creatures. StarLogo programs describe how individual creatures (not overallpopulations) behave. Thinking in terms of individual creatures seems far more intuitive,particularly for the mathematically uninitiated. Students can imagine themselves asindividual turtles/creatures and think about what they might do. In this way, StarLogoenables learners to dive into the model (Ackermann, 1996) and make use of whatPapert (1980) calls syntonic knowledge about their bodies. By observing the dynamicsat the level of the individual creatures, rather than at the aggregate level of populationdensities, students can more easily think about and understand the population oscillationsthat arise. Future versions of StarLogo will enable users to zoom in and out, making iteasier for users to shift back and forth in perspective from the individual level to thegroup level.

I refer to StarLogo models as true computational models (Resnick, 1997), sinceStarLogo uses new computational media in a more fundamental way than most computer-based modeling tools. Whereas most tools simply implement traditional mathematicalmodels on a computer (e.g., numerically solving traditional differential-equationrepresentations), StarLogo provides new representations that are tailored explicitly forthe computer. Of course, differential-equation models are still very usefuland superiorto StarLogo-style models in some contexts. But too often, scientists and educators see


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traditional differential-equation models as the only approach to modeling. As a result,many students (particularly students alienated by traditional classroom mathematics)view modeling as a difficult or uninteresting activity. What is needed is a morepluralistic approach, recognizing that there are many different approaches to modeling,each with its own strengths and weaknesses. A major challenge is to develop a better

understanding of when to use which approach, and why.

6. Decentralized Thinking

As students began working with StarLogo, they almost always assumed centralizedcauses in the patterns they observed, and they almost always imposed centralized controlwhen they wanted to create patterns. But as students continued to work on StarLogoprojects, most of them began to develop new ways of thinking about decentralization. Inalmost all cases, they developed an appreciation for and a fascination with decentralizedsystems. At one point, while we were struggling to get our termite program working, Iasked Callie if we should give up on our decentralized approach and program the termites

to take their wood chips to pre-designated spots. She quickly dismissed this suggestion:

Mitchel: We could write the program so that the termites know where thepiles are. As soon as a termite picks up a wood chip, it could just go to thepile and put it down.

Callie: Oh, thats boring!

Mitchel: Why do you think thats boring?

Callie: Cause youre telling them what to do.

Mitchel: Is this more like the way it would be in the real world?

Callie: Yeah. You would almost know what to expect if you tell them to goto a particular spot and put it down. You know that there will be threepiles. Whereas here, you dont know how many mounds there are going tobe. Or if the number of mounds will increase or decrease. Or things likethat... This way, they [the termites] made the piles by themselves. It wasntlike they [the piles] were artificially put in.

For Callie, pre-programmed behavior, even if effective, was boring. Callie preferredthe decentralized approach since it made the termites seem more independent (theymade the piles by themselves) and less predictable (you dont know how many mounds

there are going to be).

Over time, other students shared Callies fascination with decentralization, thoughthey often struggled in their efforts to use decentralized strategies in analyzing andconstructing new systems. As I worked with students, I assembled a list of guidingheuristics that students used as they began to develop richer models of decentralizedphenomena. These heuristics are not very strong. They are not rules for making senseof decentralized systems. Rather, they are loose collections of ideas associated with


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decentralized thinking. Pedagogically, they serve as good discussion points for provokingpeople to think about decentralization. They also serve as a type of measuring stick forconceptual change: as students worked on StarLogo projects, they gradually began tointegrate these heuristics into their own thinking and discourse. In this section, I discussfive of these guiding heuristics.

Positive Feedback Isnt Always Negative

When people think about the scientific idea of positive feedback, they typically thinkof the screeching sound that results when a microphone is placed near a speaker. Positivefeedback is viewed as a destructive force, making things spiral out of control. Bycontrast, negative feedback is viewed as very useful, keeping things under control.Negative feedback is symbolized by the thermostat, keeping room temperature at adesired level by turning the heater on and off as needed.

When I asked high-school students about positive feedback, most were not familiarwith the term, but they were certainly familiar with the concept. When I explained what I

meant by positive feedback, students quickly generated examples involving somethinggetting out of control, often with destructive consequences. One student talked aboutscratching a mosquito bite, which made the bite itch even more, so she scratched it somemore, which made it itch even more, and so on. Another student talked about stock-market crashes: a few people start selling, which makes more people start selling, whichmakes even more people start selling, and so on.

Despite these negative images, positive feedback often plays a crucial role indecentralized phenomena. Economist Brian Arthur (1990) points to the geographicdistribution of cities and industries as an example of a self-organizing process driven bypositive feedback. Once a small nucleus of high-technology electronics companiesstarted in Santa Clara County south of San Francisco, an infrastructure developed toserve the needs of those companies. That infrastructure encouraged even more electronicscompanies to locate in Santa Clara County, which encouraged the development of aneven more robust infrastructure. And thus, Silicon Valley was born.

For some students who used StarLogo, the idea of positive feedback provided a newway of looking at their world. One day, one student came to me excitedly. He had been indowntown Boston at lunch time, and he had a vision. He imagined two people walkinginto a deli to buy lunch.

Once they get their food, they dont eat it there. They bring it back withthem. Other people on the street smell the sandwiches and see the deli

bag, and they say, Hey, maybe Ill go to the deli for lunch today! Theywere just walking down the street, minding their own business, and all ofthe sudden they want to go to the deli. As more people go to the deli,theres even more smell and more bags. So more people go to the deli. Butthen the deli runs out of food. Theres no more smell on the street from thesandwiches. So no one else goes to the deli.


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Randomness Can Help Create Order

Like positive feedback, randomness has a bad image. Most people see randomness asannoying at best, destructive at worst. They view randomness in opposition to order:randomness undoes order, it makes things disorderly.

In fact, randomness plays an important role in creating order in many self-organizingsystems. People often assume that seeds are needed to initiate patterns and structures.In general, this is a useful intuition. The problem is that most people have too narrow aconception of seeds. They think only of preexisting inhomogeneities in theenvironmentlike a broken bridge on the highway, or a piece of food in an ants world.

This narrow view of seeds causes misintuitions. In self-organizing systems, seeds areneither preexisting nor externally imposed. Rather, self-organizing systems often createtheir ownseeds. It is here that randomness plays a crucial role. Random fluctuations actas the seeds from which patterns and structures grow. Randomness creates the initialseeds, then positive feedback makes the seeds grow. For example, the differing velocities

of cars on a highway create the seeds from which traffic jams can grow.

A Flock Isnt a Big Bird

In trying to make sense of decentralized systems and self-organizing phenomena, theidea of levelsis critically important. Interactions among objects at one level give rise tonew types of objects at another level. Interactions among slime-mold cells give rise toslime-mold clusters. Interactions among cars give rise to traffic jams. Interactions amongbirds give rise to flocks.

In many cases, the objects on one level behave very differently than objects on anotherlevel. For some high-school students, these differences in behavior were very surprising

(at least initially). For example, the students working on the StarLogo traffic project wereshocked by the behavior of the traffic jams: the jams moved backwards even though allof the cars within the jams were moving forward.

Confusion of levels is not restricted to scientifically naive high-school students. Ishowed the StarLogo traffic program to two visiting computer scientists. They were notat all surprised that the traffic jams were moving backwards. They were well aware ofthat phenomenon. But then one of the researchers said: You know, Ive heard thats whythere are so many accidents on the freeways in Los Angeles. The traffic jams are movingbackwards and the cars are rushing forward, so there are lots of accidents. The otherresearcher thought for a moment, then replied: Wait a minute. Cars crash into other cars,

not into traffic jams. In short, he believed that the first researcher had confused levels,mixing cars and jams inappropriately. The two researchers then spent half an hour tryingto sort out the problem. It is an indication of the underdeveloped state of decentralizedthinking in our culture that two sophisticated computer scientists needed to spend half anhour trying to understand the behavior of a ten-line decentralized computer programwritten by a high-school student.


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A Traffic Jam Isnt Just a Collection of Cars

For most everyday objects, it is fair to think of the object as a collection of particularparts: a chair has four particular legs, a particular seat, and so on. But not so with objectslike traffic jams. Thinking of a traffic jam as a collection of particular parts leads toconfusion. The cars composing a traffic jam are always changing, as some cars leave thefront of the jam and other join from behind. Even when all of the cars in the jam arereplaced with new cars, it is still the same traffic jam. A traffic jam can be thought of asan emergent objectit emerges from the interactions among lower-level objects (inthis case, cars).

As students worked on StarLogo projects, they encountered many emergent objects. Inthe termite example, the wood-chip piles can be viewed as emergent objects. The precisecomposition of the piles is always changing, as termites take away some wood chips andadd other wood chips. After a while, none of the original wood chips remains, but the pileis still there.

The Hills are Alive

In Sciences of the Artificial(1969), Herbert Simon describes a scene in which an ant iswalking on a beach. Simon notes that the ants path might be quite complex. But thecomplexity of the path, says Simon, is not necessarily a reflection of the complexity ofthe ant. Rather, it might reflect the complexity of the beach. Simons point: dontunderestimate the role of the environment in influencing and constraining behavior.People often think of the environment as something to be acted upon, not something tobe interacted with. People tend to focus on the behaviors of individual objects, ignoringthe environment that surrounds (and interacts with) the objects.

A richer view of the environment is important in thinking about decentralized and self-organizing systems. In designing StarLogo, I explicitly tried to highlight theenvironment. Most creature-oriented programming environments treat the environment asa passive entity, manipulated by the creature that move within it. In StarLogo, bycontrast, the patches of the world have equal status with the creatures that move in theworld. By reifying the environment, I hoped to encourage people to think about theenvironment in new ways.

Initially, some students resisted the idea of an active environment. When I explained aStarLogo ant-foraging program to one student, he was worried that pheromone trailswould continue to attract ants even after the food sources at the ends of the trails hadbeen fully depleted. He developed an elaborate scheme in which the ants, after collecting

all of the food, deposited a second pheromone to neutralize the first pheromone. It neveroccurred to him to let the first pheromone evaporate away. In his mind, the ants had totake some positive action to get rid of the first pheromone. They could not rely on theenvironment to make the first pheromone go away.


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7. New Media, New Mindsets

There is an old saying that goes something like this: Give a person a hammer, and thewhole world looks like a nail. Indeed, the ways we see the world are deeply influencedby the tools and media at our disposal. If we are given new tools and media, not only can

we accomplish new tasks, but we begin to view the world in new ways.

Often, we hardly recognize how our tools and media are influencing our ways ofviewing the world. For several centuries now, scientists have described the world interms of differential equations. Is that because differential equations are the best way torepresent and describe the world? Or is it because the common media of the era (paperand pencil) are well suited to manipulations of differential equations? Could we say:Give a scientist paper and pencil, and the whole world looks like differentialequations?

New computational media now hold the promise for radically reshaping how peoplemodel (and think about) the world. But this shift wont happen automatically. Computer

modeling will make bring profound change to the classroom only if modeling tools takefull advantage of new computational representations. Just as sculptors need to understandthe qualities of clay (or whatever material they are using), designers of computer-modeling tools need to understand their chosen medium. StarLogo, for example,leverages two new computational paradigmsmassive parallelism and object-orientedprogramming. These new paradigms offer new design possibilities: new ways to createdecentralized models. But even more importantly, these new paradigms offer newepistemological possibilities: a new decentralized framework for making sense of manyphenomena in the world.

Adding new tools to the carpenters toolkit changes the way the carpenter looks at the

world. So, too, with computational ideas and paradigms. That is the central challenge forcomputer-modeling activities in education: not only to help students create models innew ways, but also to help students develop fundamentally new ways of thinking aboutthe systems and phenomena that they are modeling.

Acknowledgments

Brian Silverman, Andy Begel, Hal Abelson, Seymour Papert, Uri Wilensky, and LarryLatour have provided inspiration and ideas for the StarLogo project. The LEGO Groupand the National Science Foundation (Grants 9153719-MDR, 9358519-RED, 9553474-RED) have provided generous financial support. Portions of this chapter were previously

published elsewhere (Resnick, 1994, 1996, 1997), and are reprinted with permission.

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Paley, W. (1802).Natural Theologyor Evidences of the Existence and Attributes of theDeity Collected from the Appearances of Nature. Oxford: J. Vincent.

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